1999 Oldsmobile Alero Vibration

Hi:
The most common cause of the vibration you described is a worn motor or trans mount. These mounts have a rubber base to absorb vibration and over time, the rubber gives allowing metal to metal contact with the car's body / frame. When the car is in gear, it places a twist on the drive line allowing the vibration to travel. When it's in park or neutral, there is no twist. Thus the vibration goes away.

Let me know if this helps.

Joe